Bring a large pot of salted water to a boil and cook the pasta until just al dente, about 8 minutes. Drain and set aside.
While the pasta cooks, heat olive oil in a skillet over medium heat. Add minced garlic and sauté until fragrant, about 1 minute, filling the kitchen with a warm aroma.
Add chopped zucchini and red bell pepper to the skillet. Sauté until slightly tender, about 5 minutes, until the vegetables are vibrant and beginning to soften.
Stir in the tomato sauce, nutritional yeast, smoked paprika, salt, and pepper. Let the mixture simmer gently for 3-4 minutes, allowing flavors to meld and the sauce to thicken slightly.
Combine the cooked pasta with the sautéed vegetables and sauce, mixing thoroughly with a spatula to coat every piece evenly.
Stir in the plant-based milk and half of the vegan cheese into the pasta mixture to add creaminess and richness.
Transfer the mixture to a greased baking dish, spreading it out evenly with the back of a spoon or spatula.
Sprinkle the remaining vegan cheese evenly over the top, creating a cheesy crust that will melt and brown during baking.
Place the dish in a preheated oven at 200°C (390°F) and bake uncovered for 20-25 minutes, until bubbling and golden around the edges.
Remove from the oven and let sit for 5 minutes. This helps the bake set and makes serving easier.
Garnish with freshly chopped herbs if desired, and serve hot to enjoy the comforting, cheesy vegan pasta bake.